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Sbornik: Mathematics, 2008, Volume 199, Issue 7, Pages 1009–1031
DOI: https://doi.org/10.1070/SM2008v199n07ABEH003951 (Mi sm3853) 		 
This article is cited in 2 scientific papers (total in 2 papers)

An explicit formula for the number of classes of primitive hyperbolic elements in the group $\Gamma_0(N)$

V. V. Golovchanskii, M. N. Smotrov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
English version PDF (376 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM2008v199n07ABEH003951
Abstract: An explicit formula expressing the number of classes of primitive hyperbolic elements in the congruence subgroup $\Gamma_0(N)$ (the number of closed geodesics) in terms of the number of equivalence classes of indefinite binary quadratic forms is obtained. The well-known formulae for the numbers of classes of elliptic and parabolic elements in $\Gamma_0(N)$ are special cases of this formula.
Bibliography: 11 titles.
Received: 15.03.2007 and 17.03.2008
Russian version:
Matematicheskii Sbornik, 2008, Volume 199, Number 7, Pages 63–84
DOI: https://doi.org/10.4213/sm3853
Bibliographic databases:
UDC: 511.342.2+512.817.2+514.774.8
MSC: Primary 30F35; Secondary 20H05, 20H10
Language: English
Original paper language: Russian
Citation: V. V. Golovchanskii, M. N. Smotrov, “An explicit formula for the number of classes of primitive hyperbolic elements in the group $\Gamma_0(N)$”, Mat. Sb., 199:7 (2008), 63–84; Sb. Math., 199:7 (2008), 1009–1031
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:58
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